Biocompatible, biodegradable polymers for various biomedical applications such as those used in sutures and tissue engineering have been described in “Functionalized Polyester Graft Copolymers,” Hrkach et al., U.S. Pat. No. 5,654,381, issued Aug. 5, 1997. Poly-dl-lactide grafted with acrylic acid was prepared and used to bind, covalently, proteins and peptides to the polyacrylic graft [G. C. M. Steffens et al., Biomaterials, 23, 3523 (2002)]. In spite of the great interest in functionalized, degradable (or absorbable) polymers, the prior art was limited to a selected few homopolymers. Accordingly, relatively new absorbable copolyesters, which are being explored in many biomedical and pharmaceutical applications, have been ignored as precursors of functionalized systems. Among these precursors are high-compliance, absorbable copolyesters used in the prior art for the production of fibers and films with unique properties as biomedical devices [Bezwada et al., U.S. Pat. No. 5,470,340 (1995), U.S. Pat. No. 5,133,739 (1992); Shalaby, U.S. Pat. No. 6,342,065 (2002), U.S. Pat. No. 6,255,408 (2001); Shalaby and Jamiolkowski, U.S. Pat. No. 4,689,424 (1987)]. Other families of potentially absorbable precursors are segmented polyetheresters, which have been used to produce novel types of absorbable fibers and films and also as vehicles for the controlled delivery of bioactive agents in the form of liquids, gels, and semi-solids [Bezwada et al., U.S. Pat. No. 5,047,048 (1991); Shalaby, U.S. Pat. No. 6,413,539 (2002).] Awareness of the importance of the potential value-added by introducing useful functional groups into the aforementioned segmented copolymers and other similar systems evoked the pursuit of the functionalized polymers, subject of this invention. Accordingly, the present invention deals with absorbable, segmented copolyesters and block copolymers of polyalkylene glycols containing predetermined amounts of functional side groups on their main chains.